 # Doppler Shift

## What is a Doppler Shift?

Doppler shift is also known as the Doppler effect is characterized as a change in wavelength or wave frequency with respect to the observer who is in motion relative to the wave source. The phenomenon was described by the Austrian physicist Christian Doppler in the year 1842.

What happens when an ambulance has passed you? Why does the siren 's tone change? It gets louder as it approaches, but another characteristic of sound changes as well. The pitch is higher when it moves towards you (think of a whining noise) and lower when it moves away (think of a deep voice). This change in pitch has to do with the frequency of waves, or how many waves pass through an area per unit of time.

In the case of an ambulance, you 're still standing and the ambulance is approaching you. As the sound waves move towards you, they are compressed and the frequency increases, so you hear a higher pitch. However, when the ambulance moves away from you, the sound waves spread further apart and the frequency gets lower, so you hear a lower pitch. This change in the frequency of sound waves due to movement is called the Doppler shift, also known as the Doppler effect.

The Doppler effect is observed whenever the wave source moves with respect to the observer. The Doppler effect can be defined as the effect created by a moving wave source in which there is an apparent upward shift in frequency for observers to whom the source is approaching and a clear downward shift in frequency for observers from whom the source is receding. It is important to remember that the effect is not due to a real shift in the frequency of the source.

The Doppler effect can be observed for any wave type-water wave, sound wave, lightwave, etc. Because of our experiences with sound waves, we are most familiar with the Doppler effect. You may remember an incident in which a police car or emergency vehicle was driving to you on the highway. As the car approached with its siren blast, the pitch of the siren sound (a measure of the siren 's frequency) was high; and then, unexpectedly, after the car passed by, the pitch of the siren sound was low. That was the Doppler effect-an an apparent shift in the frequency of a sound wave produced by a moving source.

### What is Doppler Shift Formula?

$f = (\frac{c \pm vr}{c \pm vs})fo$

Where,

• C is the amplitude of the wave in the medium;

• vr is the speed of the receiver relative to the medium (positive if the receiver moves towards the source and negative if it moves in the opposite direction)

• vs is the velocity of the source relative to the medium (positive if the source moves away from the receiver and negative if it moves in the opposite direction)

• f is the frequency observed

• f0 is the frequency emitted.

Above is the Doppler shift or Doppler effect formula which explains the relationship between the observed frequency and the emitted frequency where the velocity of the source and receiver is lower than the velocity of the waves in the medium. The following is the formula when the receiver and source speeds are relatively smaller than the wave velocity:

Observed Frequency:

$F =(1 + \frac{\triangle v}{c})f_{0}$

Change in Frequency:

$\triangle f = \frac{\triangle v}{cf_{0}}$

Where, Δf = f − f0, Δv = vr − vs velocity of the receiver relative to the source (positive when the source and the receiver moving towards each other).

### Sirens

The concept behind siren is that it starts at a pitch higher than its stationary pitch as it travels down from the observer, and again as it recedes from the observer, it continues from a lower pitch than its stationary pitch. It is used in emergency vehicles. The velocity of Siren is given as:

where ፀ is the angle between the object’s line of sight and the forward velocity.

### The Doppler Effect in Astronomy

The Doppler effect is of considerable interest to astronomers who use information on the change in the frequency of electromagnetic waves generated by moving stars in our galaxy and beyond to gain information about these stars and galaxies. The assumption that the universe is expanding is, in part, based on measurements of electromagnetic waves produced by stars in distant galaxies. In addition, the application of the Doppler effect will assess the precise details of stars within galaxies.

Galaxies are clusters of stars that typically rotate around a center of mass. Electromagnetic radiation released by these stars in a distant galaxy will appear to be moving downwards in frequency (red shift) if the star rotates in its cluster in a direction away from Earth. At the other hand, there is an upward change in the frequency (blue change) of the detected radiation as the star rotates in a direction to the Moon.

### Velocity Profile Measurement

Ultrasonic Doppler Velocimeter is used to calculate the real-time performance velocity profile of any liquid containing suspended particles, such as dust, emulsions and gas bubbles. The flow can be pulsating, laminar or turbulent, oscillating or steady.

Q1 - Explain 'Doppler Effect'.

Ans - Doppler Effect refers to a change in the frequency of waves during the relative motion between the wave source and its observer. It was discovered by Christian Johann Doppler, who identified it as a cycle of increasing or decreasing starlight that depends on the relative movement of the star.

Q2 - What is the Use of the Doppler Effect?

Ans - The use of Doppler Effect in astronomy in light waves relies on the fact that the spectra of the stars are not constant. Different stars show different absorption lines at defined frequencies, but the Doppler Effect is only detectable when these absorption lines are away from these defined frequencies.

There are various applications of the Doppler Effect. It is used in:

1. Sirens

2. Astronomy